The mogul mayor; Mike Bloomberg adds it all up.

Michael Bloomberg is impatient with words but likes numbers. His public appearances, while notable for their brevity, nearly always feature some figure or factlet that he finds salient -- the size of the city's police force, say (forty thousand officers), or the year the World Trade Center was conceived (1960), or the proportion of New Yorkers who are African-American (one in four). Among the first pledges that he made upon taking office was that every month he would post on the Internet an exact head count of his staff. Current total: four hundred and ninety-seven.

Bloomberg himself is New York's hundred-and-eighth mayor, a job he acquired by spending more money on his campaign than anyone in the history of the country (seventy-four million dollars). He recently turned sixty, and, based on his stake in Bloomberg L.P., the privately held financial-data empire that he founded, he is, according to Forbes, the seventy-second-richest person in the world, up ten places from last year. Bloomberg's driver's license puts his height at five feet ten, which means that he is either taller than he looks or shorter than he says. His girlfriend, Diana Taylor, is five feet nine and a half, and when they stand next to each other, as the News recently pointed out, she towers over him.

Every new mayor recasts the job in his own image; Bloomberg, perhaps not surprisingly, has already pushed this further than most. He has, for example, declined to move into Gracie Mansion. (The city-owned residence, completed in 1804, has not, Bloomberg explained, "had a face-lift for some time.") Instead, he has opted to remain in his five-story town house, on East Seventy-ninth Street, which features a foyer done in Egyptian porphyry, French Empire sideboards, and a library whose hue Bloomberg's decorator once compared to "a bottle of cognac held up to the light, all glowing cognac colors." Shortly after his victory in November, Bloomberg held an intimate get-acquainted dinner for the five borough presidents at his town house. He served Chateau Haut-Brion, which retails for at least a hundred and fifty dollars a bottle, and sent each guest home with a giant cookie decorated in icing with the seal of his or her borough. The fifty-one members of the City Council he invited over for cocktails. Afterward, some of them wondered about their host's decision to serve caviar at a time when the city seems headed toward the worst fiscal crisis since perhaps the Depression, but in the end the consensus was that it had been the right thing to do. The Mayor has four other homes, in Westchester, Vail, London, and Bermuda. When he takes the weekend off, he refuses, on principle, to say where he's headed.

Bloomberg is the first to point out that, according to the numbers, New York is in deep trouble. In February, when he presented the outline of his spending plan, he dispensed with the usual preliminaries and instead of low-balling the problem, as is City Hall custom, forecast a budget gap bigger than anyone had predicted. Bloomberg put the size of the gap at $4.8 billion, which is, by coincidence, roughly the size of his own personal fortune. To meet a shortfall of this magnitude, he pointed out, sacrifice would be required from everyone. "The two hundred and fifty thousand people who work for New York City do a pretty good job," he said. "So you can't just rush in and say, 'Let's just do things better.' " (Later, the Mayor qualified this, saying that a more accurate number to use for the city workforce might be three hundred and six thousand or, alternatively, three hundred and sixty-three thousand.)

Depending once again on how you count, the mayoralty is either Bloomberg's third or fourth career. In the previous ones, he was so enormously successful that he was often asked to share his secret for getting ahead. Bloomberg is fond of aphorisms, and the advice he used to dispense consisted of lines like "Always be building," "Do what you love," and "Bring a gun to a knife fight." Just by virtue of winning the election, he has already exceeded what was expected of him politically, and his first hundred days in office have mostly gone smoothly. As mayor, he has made strong appointments, reorganized City Hall, calmed the bond-rating agencies, and reached out to many groups in New York that are not normally considered the constituencies of a Republican billionaire. How he will manage the graver challenges that lie ahead is obviously the central question of the next four years, but it is not one that Bloomberg himself seems in any way troubled by. "He doesn't have self-doubts," Morris Offit, who runs a capital-management firm and is an old friend of the Mayor's, told me. "There's no hand-wringing. It goes back to the trader's mentality: you take a shot, and if you're wrong you go on to the next one."

On an average day, Bloomberg appears at three or four events around the city. One morning not long ago, his first stop was a topping-out ceremony for the huge new AOL Time Warner headquarters, which is rising above Columbus Circle. The project, conceived in a happier, more expansive moment for New York, is also to include condominiums, a Mandarin Oriental hotel, and a new home for Jazz at Lincoln Center. Hundreds of people were milling around the sixth floor of the unfinished building, which, lacking walls, provided a spectacular view of Central Park.

As soon as the Mayor arrived, wearing a gray suit and tasselled loafers, he was ushered to a makeshift stage. He offered his factlet, declaring, not altogether accurately, "Seventy-five years ago next month, there was an American flag raised as part of the topping-out ceremony on the Empire State Building," and added a few upbeat words of praise: "We've really got a wonderful thing for our children, and thank you." Eventually, an American flag went up over the building, while Wynton Marsalis played "Buddy Bolden's Blues," but by that point Bloomberg was already long gone.